Impedance Optimization for Uncertain Contact Interactions through Risk Sensitive Optimal Control

Bilal Hammoud, Majid Khadiv, Ludovic Righetti

Research output: Contribution to journalArticlepeer-review


This letter addresses the problem of computing optimal impedance schedules for legged locomotion tasks involving complex contact interactions. We formulate the problem of impedance regulation as a trade-off between disturbance rejection and measurement uncertainty. We extend a stochastic optimal control algorithm known as Risk Sensitive Control to take into account measurement uncertainty and propose a formal way to include such uncertainty for unknown contact locations. The approach can efficiently generate optimal state and control trajectories along with local feedback control gains, i.e. impedance schedules. Extensive simulations demonstrate the capabilities of the approach in generating meaningful stiffness and damping modulation patterns before and after contact interaction. For example, contact forces are reduced during early contacts, damping increases to anticipate a high impact event and tracking is automatically traded-off for increased stability. In particular, we show a significant improvement in performance during jumping and trotting tasks with a simulated quadruped robot.

Original languageEnglish (US)
Article number9387077
Pages (from-to)4766-4773
Number of pages8
JournalIEEE Robotics and Automation Letters
Issue number3
StatePublished - Jul 2021


  • Humanoid and bipedal locomotion
  • legged robots
  • motion control
  • optimization and optimal control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Biomedical Engineering
  • Human-Computer Interaction
  • Mechanical Engineering
  • Computer Vision and Pattern Recognition
  • Computer Science Applications
  • Control and Optimization
  • Artificial Intelligence


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